|
Author |
Message |
|
TAGS:
|
|
|
SVP
Joined: 04 May 2006
Posts: 1946
Schools: CBS, Kellogg
Followers: 10
Kudos [?]:
168
[0], given: 1
|
If a, b and c are integers such that b > a, is b+c > a [#permalink]
 26 May 2009, 02:46
Question Stats:
31% (02:35) correct
68% (01:21) wrong based on 3 sessions
If a, b and c are integers such that b > a, is b+c > a ? (1) c > a (2) abc > 0
_________________
Find out what's new at GMAT Club - latest features and updates
Last edited by Bunuel on 10 Aug 2012, 00:22, edited 1 time in total.
Edited the question.
|
|
|
|
|
|
|
Director
Joined: 27 Jun 2008
Posts: 552
WE 1: Investment Banking - 6yrs
Followers: 1
Kudos [?]:
39
[0], given: 92
|
sondenso wrote: If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0 E a = -4 or 3 b = -3 or 4 The above satifies b>a, using - or + as examples. (1) c>a c = -2 or 4 Insuff (2) abc>0 This means either 2 of the intergers are negative or all of the intergers are positive. Insuff
|
|
|
|
|
|
Manager
Joined: 14 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 3
Kudos [?]:
18
[0], given: 1
|
sondenso wrote: If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0 b>a <==> 0>a-b <==> a-b is negative Question:(b+c>a)? Question:(c>a-b)? Question:(c >= 0)? (1) Insufficient, as a-b<0 could mean that a<0 or a>0, which means c<0 or c>=0. (2) We have an even # of negatives, ie 0/2. If we have 0 negatives, then sufficient. Again if we have 2 insufficient. I can see the pattern, the answer is E. Here are the Yes/No cases: Yes: 4 5 7 No: -9 3 -10 Final Answer, E.
_________________
Hades
|
|
|
|
|
|
Manager
Joined: 10 Aug 2008
Posts: 77
Followers: 1
Kudos [?]:
13
[0], given: 0
|
For me its straight A)
|
|
|
|
|
|
Manager
Joined: 11 Apr 2009
Posts: 170
Followers: 2
Kudos [?]:
13
[0], given: 5
|
why cant it be C?
1. b>a and c>a and abc>0:
If a<0, b can be less than or greater than 0.
If a<0, b<0 then c>0 (a=-6, b=-4, c=2) => b+c >a
If a<0, b>0, c<0 (a=-3, b=5, c=-1) => b+c >a
If all are positive, then also b+c >a.
Hence, C.
Are there any assumptions which do not satisfy both conditions simultaneously?
What is the OA?
|
|
|
|
|
|
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
Posts: 211
Schools: Harvard, Penn, Maryland
Followers: 4
Kudos [?]:
19
[0], given: 3
|
The answer is C
statement 1 does work for positives, but not for negatives. a= -2 b= -1 c= -1.
statement 2 doesnt work on its own because c could be way less than a, negating b,
a= -3 b=2 c= -5
however, both together mean that there can only be two negatives, and c must be larger than A.
for any value A, negative or not, two values that are greater than it with one positive are going to together be greater than A.
if A is positive = a=2, c=3, b=3, a=1 b=2 c=2
if A is negative = a= -3, c= -2, b=1, a= -2 b=-1 c=1
There is no solution with (1) and (2) true that doesn't end up with B + C > A
gmatprep is right
|
|
|
|
|
|
Manager
Joined: 11 Apr 2009
Posts: 170
Followers: 2
Kudos [?]:
13
[0], given: 5
|
Has anybody considered taking both the conditions 1 and 2 together? What is the OA for this? I still think its C.
|
|
|
|
|
|
Senior Manager
Joined: 08 Jan 2009
Posts: 338
Followers: 2
Kudos [?]:
42
[0], given: 5
|
b>a
stmt 1 :
c>a so b+c>2a
we cannot tell whether b+c >a may or may not. So insufficient.
stmt 2 :
abc>0 and b >a
a = +ve b = +ve c =+ve so definetly b+c > a
a = -ve b = -ve c = +ve so definetly b+c > a. ( since c =+ve and b>a)
a = -ve b = +ve c = -ve ( here it is just the opposite u know b =+ve but do not know c>a).so u cant tell whether b+c > a
Combing : yes u know you have got what u wanted so C.
Thanks gmatprep09 and dk94588.
|
|
|
|
|
|
Senior Manager
Joined: 16 Apr 2009
Posts: 252
Schools: Ross
Followers: 1
Kudos [?]:
10
[0], given: 10
|
I agree C is the answer. If a,b and c and positive,it is possible.
_________________
Keep trying no matter how hard it seems, it will get easier.
|
|
|
|
|
|
CEO
Joined: 29 Aug 2007
Posts: 2530
Followers: 41
Kudos [?]:
358
[0], given: 19
|
|
|
|
|
|
|
Manager
Joined: 28 Jan 2004
Posts: 210
Location: India
Followers: 2
Kudos [?]:
9
[0], given: 4
|
tkarthik wrote -
c>a so b+c>2a
we cannot tell whether b+c >a may or may not. So insufficient
If b+c>2a how in the world can it not be > a !!!! I m confused.Can you pls. elaborate or give example numbers.
|
|
|
|
|
|
Senior Manager
Joined: 08 Jan 2009
Posts: 338
Followers: 2
Kudos [?]:
42
[0], given: 5
|
Hi mdfrahim
you need to take some negative value.
Say a,b,c are +ve then b+c > a and b+c>2a
say b = -2 c = -3 a =-4 ( c> a and b > a)
b + c = -5 which less than a but will be greater than 2a.
I meant to say this only. Hope i have made it clear.
|
|
|
|
|
|
Manager
Joined: 28 Jan 2004
Posts: 210
Location: India
Followers: 2
Kudos [?]:
9
[0], given: 4
|
Thx. TKathik, you made it clear.
|
|
|
|
|
|
Manager
Joined: 14 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 3
Kudos [?]:
18
[0], given: 1
|
Whoops the answer is C If you look at both together, we have that b>a & c>a. from (1) we get b+c>2a and we're almost sufficient, but only if 2a>a. Well if a<0, no, but if a>0, yes. (2) tells us that 0 or 2 are negative. If all 3 are positive, sufficient. Now if 2 are negative, then a has to be negative as well. Suppose a were positive-- then b/c would be negative, and b>a & c>a would be false. Hence a has to be positive. (C) Very tricky
_________________
Hades
|
|
|
|
|
|
Manager
Joined: 11 Sep 2009
Posts: 111
Followers: 1
Kudos [?]:
5
[0], given: 0
|
Re: Property of Integers, Inequalities [#permalink]
23 Oct 2009, 00:02
(1) because b and c both can be negative, thus (1) is insufficient
(2) insufficient for example, a = -2, b = 1, c = -4
Both are sufficient because either b or c is always greater than a.
|
|
|
|
|
|
Manager
Joined: 02 Nov 2009
Posts: 144
Followers: 2
Kudos [?]:
4
[0], given: 97
|
Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
09 Aug 2012, 23:40
Bunuel can you please provide your method
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11616
Followers: 1802
Kudos [?]:
9600
[2] , given: 829
|
Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
10 Aug 2012, 01:15
2
This post received
KUDOS
If a, b and c are integers such that b > a, is b+c > a ?Question: is b+c > a ? --> or: is b+c-a > 0? (1) c > a. If a=1, b=2 and c=3, then the answer is clearly YES but if a=-3, b=-2 and c=-1, then the answer is NO. Not sufficient. (2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be a (because if a is not negative, then b is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider a=-3, b=1 and c=-4 and . Not sufficient. (1)+(2) We have that b > a, c > a ( c-a>0) and that ether all three unknowns are positive or a and any from b and c is negative. Again for the first case the answer is obviously YES. As for the second case: say a and c are negative and b is positive, then b+(c-a)=positive+positive>0 (you can apply the same reasoning if a and b are negative and c is positive). So, we have that in both cases we have an YES answer. Sufficient. Answer: C.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 15 Nov 2012
Posts: 7
Followers: 0
Kudos [?]:
0
[0], given: 3
|
Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
26 Feb 2013, 06:52
Bunuel wrote: If a, b and c are integers such that b > a, is b+c > a ?
Question: is b+c > a ? --> or: is b+c-a > 0?
(1) c > a. If a=1, b=2 and c=3, then the answer is clearly YES but if a=-3, b=-2 and c=-1, then the answer is NO. Not sufficient.
(2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be a (because if a is not negative, then b is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider a=-3, b=-4 and c=1. Not sufficient.
(1)+(2) We have that b > a, c > a (c-a>0) and that ether all three unknowns are positive or a and any from b and c is negative. Again for the first case the answer is obviously YES. As for the second case: say a and c are negative and b is positive, then b+(c-a)=positive+positive>0 (you can apply the same reasoning if a and b are negative and c is positive). So, we have that in both cases we have an YES answer. Sufficient.
Answer: C. In 2nd case you have taken a=-3,b=-4,c=1. But the problem clearly stating that b must be grater than a ( b>a). But you have taken in a different way which might result in wrong answer.Correct me if i am wrong?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11616
Followers: 1802
Kudos [?]:
9600
[0], given: 829
|
Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
26 Feb 2013, 07:42
mannava189 wrote: Bunuel wrote: If a, b and c are integers such that b > a, is b+c > a ?
Question: is b+c > a ? --> or: is b+c-a > 0?
(1) c > a. If a=1, b=2 and c=3, then the answer is clearly YES but if a=-3, b=-2 and c=-1, then the answer is NO. Not sufficient.
(2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be a (because if a is not negative, then b is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider a=-3, b=-4 and c=1. Not sufficient.
(1)+(2) We have that b > a, c > a (c-a>0) and that ether all three unknowns are positive or a and any from b and c is negative. Again for the first case the answer is obviously YES. As for the second case: say a and c are negative and b is positive, then b+(c-a)=positive+positive>0 (you can apply the same reasoning if a and b are negative and c is positive). So, we have that in both cases we have an YES answer. Sufficient.
Answer: C. In 2nd case you have taken a=-3,b=-4,c=1. But the problem clearly stating that b must be grater than a ( b>a). But you have taken in a different way which might result in wrong answer.Correct me if i am wrong? The values of b and c should be switched. It should be a=-3, b=1 and c=-4. Typo edited thank you.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: If a, b and c are integers such that b > a, is b+c > a
[#permalink]
26 Feb 2013, 07:42
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
a+b)^2 * (b-c)] / >= 0 ? 1- a>b 2- b>c
|
Paul |
4 |
06 Nov 2004, 19:08 |
|
|
|
|
Is (a/d)*(b/e)*(c/f) > (b/d)*(c/e) ? (1) bc > de (2) a
|
forumsmba |
4 |
02 Dec 2004, 16:48 |
|
|
|
|
If a, b and c are integers such that b > a, is b+c > a
|
kevincan |
8 |
25 Sep 2007, 07:33 |
|
|
|
|
If A, B and C are integers such that B>A, is B+C > A?
|
netcaesar |
3 |
25 Jan 2008, 11:08 |
|
|
2
|
|
if a>0, b>0, c>0, is a(b-c)=0? I. b-c = c-b II. b/c
|
tejal777 |
3 |
21 Aug 2009, 19:24 |
|
|
|
|
|
|
close
